Original article
Optimal design of a groundwater monitoring network in Daqing, China Y. Wu
Abstract In the Daqing region of China there are 34 groundwater well fields with a groundwater withdrawal of 81.9·104 m3/d. Due to overabstraction of the groundwater resources from the 1960s to present, a cone of depression up to 4,000 km2 has formed in the area. To monitor the change in the groundwater environment, it is necessary to design an effective groundwatermonitoring network. The sites for monitoring groundwater level were selected by applying the finite-element method coupled with Kalman filtering to the area in which the groundwater resources have been extensively exploited. The criterion is a threshold value of the standard deviation of estimation error. This threshold value is determined by the tradeoff between maximum information and minimum cost, in which the maximum information is characterized by the standard deviation and the minimum cost is equivalent to the number of observation wells. The groundwater flow model was calibrated by an optimal algorithm coupled the finite-element method with Kalman filtering by using the data from 16 observation wells from 1986 to 1993. A simulation algorithm coupled with the finite-element method with Kalman filtering analyzed the location data obtained from the existing 38 observation wells in the same region. The spatial distribution of standard deviation of estimation error is computed and the locations that have the maximum standard deviation are selected as additional sites for augmenting the existing observational well network at a given threshold
Received: 7 February 2003 / Accepted: 7 August 2003 Published online: 15 October 2003 ª Springer-Verlag 2003 Y. Wu Cold and Arid Regions Environmental and Engineering Research Institute of CAS, 730000 Lanzhou, China E-mail:
[email protected] Tel.: +086-931-4967155 Fax: +086-931-8275241
Present address: Y. Wu Xi’an University of Technology, 710048 Xi’an, China
value of the standard deviation surface. Based on the proposed method for selecting a groundwater level monitoring network, an optimal monitoring network with 88 observation wells with the measurement frequency of 12 times per year is selected in the Daqing region of China. Keywords Observation well Æ Coupled finite-element method and Kalman filtering Æ Optimal groundwater monitoring network Æ Daqing region of China
Introduction Due to the increased concern for the environment, the monitoring effort for both surface water and groundwater has expanded significantly. To understand the change of groundwater environment caused by over-abstraction of groundwater resources, it is necessary to set up a groundwater-monitoring network. According to the design purpose of groundwater monitoring, the monitoring of groundwater can be separated into the groundwater quality-monitoring network and groundwater level-monitoring network (Loaiciga 1989; Loaiciga and others 1992; Wu 1992; Zidek and others 2000). Based on a network design algorithm for hydrological monitoring network design, the methods employed can be divided into three categories: those which include the time series analysis and regression methods (Crawford 1979;Made 1986), the Kriging method (Carrera and others 1984; Bogardi and others 1985; Knopman and Voss 1989; Loaiciga 1989; Wu 1992) and the Kalman filtering method (Van Geer 1982; Wu 1992; Wu and Bian 2003). In time series analysis, the value of an element of a measurement series is estimated from other elements of that series or from other measurement series, without using any deterministic information about the hydrological process. Estimation with time series analysis is based on auto-correlations and cross-correlations. Models based on time series analysis are restricted to variables with Gaussian distributions or to variables that can be transformed to Gaussian distributions. With time series analysis, estimates of variables can only be calculated for points in time at sites where measurements of the variable
DOI 10.1007/s00254-003-0907-x Environmental Geology (2004) 45:527–535
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are being taken. The spatial coherence of the measurements is not taken into account. In the regression method, the parameters of an analytical function are estimated from such measurements that the difference between the function and the measurements is minimal in the least squares sense. The assumption that the measurements of each individual variable are independent is restricted to the regression method. Time series analysis and regression methods are often applied in the design of precipitation, rainfall-runoff, and surface water monitoring networks (Crawford 1979; Bras 1979; Adamouski and Hamory 1983; Made 1986). Kriging provides a possible spatial interpolation technique for time-independent variables. The values of the variable under consideration at a location are estimated from a local weighted average of the observations. The weights are determined in such a way that the estimation is optimal in the sense of the least estimation error variance. In addition to the spatial estimate of the variable, the variance of the corresponding estimation error is also calculated. The estimation error associated with values interpolated from a set of measured hydrogeological variable values can be used in network design to reduce the uncertainty of the interpolated values. Two types of methods have been suggested in which interpolation error serves as a measure of network performance. The first type is a trial and error method in which locations with the largest estimation error are selected as new measurement sites (Journel and Huijbregts 1978; de Marsily 1986). The second type is an optimization method in which estimation error at a point or set of points is the objective to be minimized, and potential measurement locations are the decision variables (Bogardi and others 1985; Carrera and Szidarovzsky 1985; Knopman and Voss 1989; Solomatine 1999; Hsu and Cheng 2000; Pinder and others 2002; Reed 2002; Dorn and Ranjithan 2003). The Kriging technique, without the flow equations and time dimension but with a polynomial approximation of the drift, has been applied in the design of monitoring networks for groundwater, such as for optimum selection of sites for monitoring groundwater level (Carrera and others 1984; Prakash and Singh 2000; Rouhani 1985; Spruill and Candela 1990). The above-mentioned methods all attempt to minimize hydrogeological variable estimation error solely on the basis of the interpolation procedure used for estimation. A major drawback of these methods is that they are based only on measured hydrogeological variables and do not rely on any knowledge of the groundwater system dynamics. Wood and McLaughlin (1984) combined groundwater simulation and Kriging to reduce the size of an existing measurement network. Modeling errors, the difference between measured and predicted state variables, were kriged to obtain modeling errors and uncertainty estimates at unmeasured locations. Wilson and others (1978) combined groundwater flow modeling and the Kalman filter for optimal design of the groundwater monitoring. The Kalman filtering combines the time dependence and the spatial coherence of the hydrological process. It can be used to select optimum sites and observational frequency for monitoring groundwater. 528
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The uncertainty of numerical groundwater simulations and distributed parameters can be taken into account (Van Geer 1982; Zhou and others 1991; Wu 1992; Zhou and Van Geer 1992). Another method is the coupling of the Kalman filter and the finite-difference method. The alternative network with the standard deviation of estimation error approximated a given threshold value at each interpolated location is accepted as the optimal network. But, the selection of threshold value of the standard deviation of estimation error is not described in previously published literature. In this paper, an algorithm coupled Kalman filter and finite-element method is proposed and applied for the network design of groundwater monitoring in regions with a larger intensity of groundwater abstraction. In the present paper, optimal network analysis is carried out using the standard deviation of estimation error obtained from a simulation algorithm that couples the Kalman filter and finite element methods. The criterion is a threshold value of the standard deviation of estimation error. This threshold value is determined by the tradeoff between maximum information and minimum cost, in which the maximum information is characterized by the standard deviation and the minimum cost is equivalent to the number of observation wells.
Methodology A two-dimensional unsteady groundwater flow in a heterogeneous, anisotropic, and semi-confined aquifer is considered in this study; the aquifer is bounded by semi-pervious and impervious layers above and below the aquifer, respectively. An aquifer with confined groundwater is always saturated with groundwater and the governing equation can be stated by: @ @H @ @H 1 ðKx M Þ þ ðKy M Þ þ ðHu HÞ þ Qðx; y; tÞ @x @x @y @y c @H ð1Þ þ Wh ðx; yÞ ¼ S @t The following initial and boundary conditions are: Hðx; y; 0Þ ¼ H0 ðx; yÞ; ðx; yÞ 2 X
ð2aÞ
Hðx; y; tÞ ¼ H1 ðx; y; tÞ; ðx; yÞ 2 C1
ð2bÞ
Kx M cosðx; nÞ
@H @H þ Ky M cosðy; nÞ @x @y
¼ qðx; y; tÞ; ðx; y; tÞ 2 C2
ð2cÞ
where Hu is the water table in an unconfined aquifer which is a spatio-temporal function [L]; c=M’/K’ is the hydraulic resistance of the semi-pervious layer [T], M’ is the thickness of the semi-pervious layer [L], K’ is the hydraulic conductivity in the semi-pervious layer [LT)1]; H is the hydraulic head in confined aquifer which is a spatio-temporal function [L]; Kx, Ky are the hydraulic conductivity in the x-direction and y-direction in the confined aquifer, respectively [LT)1];
Original article
M is the thickness of confined aquifer [L]; S is the storage coefficient of confined aquifer; Q(x,y,t) is the source (or sink) term in the flow domain [LT)1]; x and y are the space variables [L]; t is the time variable [T]; W is the flow domain; C1 ; C2 are the boundaries specifying hydraulic head and flux, respectively; H0(x,y) is the initial hydraulic head in the flow domain [L]; H1(x,y,t) and q (x,y,t) are the hydraulic head [L] and flux [L2T)1] at the specified boundaries (C1 ; C2 ), respectively; and Wh(x,y) is the system noise function [LT)1]. In general, a numerical scheme is required to obtain the solution of Eqs. (1) and (2a, 2b, 2c). Using the Galerkinbased finite element method, Eq. (1) leads to the following global matrix system of N, the total number of nodes, equations: dH GHþD ¼F ð3Þ dt
The hydraulic head is measured in a number of observation wells. If there are m observation wells in the flow domain, a measurement vector can be given by: Y k ¼ Ck H k þ Vk
ð7Þ
where Yk is the measurement vector at time k; Ck is the measurement matrix at time k; and Vk is the measurement error vector at time k. The system noise vector and the measurement error vector are realizations of multidimensional stochastic processes. In the derivation of the Kalman filter algorithm the following assumptions are made for the first and second order central moments. The expected values of the system noise vector and the measurement error vector can be given by (Van Geer 1982): EðWk Þ ¼ W; EðVk Þ ¼ 0
ð8Þ
with its components written in indicial notation:
and, the covariance matrices are given by:
X Z @UI @UJ GIJ ¼ Kij M @xi @xj e
E½ðWk WÞðWl WÞT ¼ dkl Qk ; EðVk VTl Þ k ÞT ¼ 0 ¼ dkl Rk ; E½Vk ðWk W
ð4aÞ
Xe
DIJ ¼
XZ e
FI ¼
ð4bÞ
SUI UJ
Xe
XZ e
Xe
XZ XZ UI Qþ U I Wh UI qn e
Xe
e
ð4cÞ
Ce
where the subscripts I,J=1,2,..., N denote nodal indices, i,j=1,2,..., ND are spatial indices of the Cartesian coordinates, Xe is the finite element domain, UI is the nodal basis function, called the trial space, xi are the Cartesian spatial coordinates, Kij is the hydraulic conductivity tensor in the deep aquifer, qn corresponds to the normal fluid flux directed positive outward on C. For stability reasons only implicit time discretizations are appropriate for the present class of problems. The implicit form of Eq. (3) reads:
where dkl ¼
ð9Þ ¼ 0; k 6¼ l ¼ 1; k ¼ l
The simulation algorithm of Eqs. (6) and (7) can be obtained under the assumption conditions (8) and (9) from (Van Geer 1982; Wu 1992): Pk=k1 ¼ Ak Pk1 ATk þ Qk
ð10aÞ
Kk ¼ Pk=k1 CTk fCk Pk=k1 CTk þ Rk g1
ð10bÞ
Pk ¼ ðI Kk Ck ÞPk=k1
ð10cÞ
P0 ¼ VarðH0 Þ
ð10dÞ
where Kk is the Kalman gain matrix at time k; Pk/k-1 is the covariance matrix of the prediction error; and Pk is the covariance matrix of the optimal estimation error. The simulation is based on the fact that the covariance matrices can be calculated without estimating the state ðG þ D=DtÞHkþ1 ¼ ðD=DtÞHk þ Qkþ1 þ Wkþ1 ð5Þ vector. The fact that the simulation algorithm is calculated without real data makes it possible to introduce fictive where G is the permeability matrix; D is the storage measuring points and fictive measurement frequencies to matrix; Qk+1 is the source (or sink) term vector including calculate a fictive standard deviation surface. This can be leakage term at time k+1; Wk+1 is the system noise vector achieved by changing the measurement matrix C . Any k at time k+1; Hk+1 and Hk are the hydraulic head vectors at combination of measuring points and frequencies can be times k+1and k, respectively; and Dt is the time step. calculated with the simulation algorithm. Therefore, the Eq. (5) can be simplified to: simulation algorithm is a very powerful tool for improving and designing the monitoring network. Hkþ1 ¼ AHk þ BFkþ1 þ EWkþ1 ð6Þ
where Fk+1=(U,Q)Tk+1 is the system input vector at times k+1, U is the input vector at the given hydraulic head boundary; E=(G+D(Dt))1is the coefficient matrix of the Study area system noise vector; B=(G+D/Dt))1P is the coefficient matrix of the system input, P is the coefficient matrix The study area is between 12414’10’’ E to 125E and associated with the location of input; A=(G+D/Dt))1(D/Dt) 4500’05’’ N to 4700’05’’ N and covers an area of about is the system transition matrix. 7,000 km2 is shown as Fig. 1. Daqing city is in the eastern
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Fig. 1 Location map of the study area
part of study area. This area lies in the semi-arid region of China. The annual mean precipitation and evaporation in the study area are 445 mm and 1,600 mm, respectively.
Hydrogeologic setting The stratigraphic units in the study area include the Late Cretaceous Mingshui Group (K2m), the Early Tertiary Yi’an Group (E2+3y), the Late Tertiary Taikang Group (N2t), the Early Quaternary Baitushan Group (Q1), the Middle Quaternary Huangshan Group (Q2), and the Late Quaternary Haerbin Group (Q3), as shown in Fig. 2. In general, the aquifers in the study area are divided into the deep confined aquifer, representing the major aquifer 530
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and the upper aquifer, also called the shallow aquifer. The deep confined aquifer consists of coarse sand and gravel formations of the Early Quaternary Baitushan Group (Q1) and semi-consolidated gravel stone formations of the Late Tertiary Taikang Group (N2t). Its thickness ranges from 20 to 140 m as shown in Fig. 2. This formation is characterized by larger voids and fragmented structures. The hydraulic permeability of the rock formation is high. The upper aquifer consists of fine sand materials of the Late Quaternary Haerbin Group (Q3). Its thickness ranges from 5 to 30 m. The semi-pervious layer between the upper aquifer and deep aquifer mainly consists of the clay formation and silt interlayers of the Middle Quaternary Huangshan Group (Q2). The thickness of the semi-pervious layer ranges from 20 to 70 m. The impermeable layer is the mudstone of the Early Tertiary Yi’an Group (E2+3y) as shown in Fig. 2.
Original article
Fig. 2 Hydrogeological section maps of the study area, 1, fine sand layer as the shallow aquifer; 2, sand clay layer as the semi-pervious layer; 3, fine sand lensoid layer; 4, coarse sand and gravel layer as the deep confined aquifer; 5, semi-consolidated gravel layer as the deep confined aquifer; 6, mudstone as the impermeable layer; 7, mudstone as the impermeable layer; 8, sandy mudstone as the impermeable layer
An application of network design Model calibration The model domain is divided into 688 triangle elements and 383 nodes and covers 7,000 km2. The time step and simulation period were taken as 30 days and 8 years from January 1986 to December 1993, respectively. The measurements from 16 observation wells were selected to calibrate the deterministic-stochastic model of the groundwater flow system. Based on the accuracy of observation instruments, observation techniques, and the skill of the observer, the standard deviation of the measurement error was fixed at 0.05 m for all observation wells. The aquifer was divided into 18 subareas to estimate
Fig. 3 Stochastic parameter subareas of the groundwater flow in the deep aquifer. Dots indicate observation wells; solid line, zero flux boundary; broken line, given hydraulic head boundary
the parameters in accordance with hydrogeologic conditions. From Fig. 3 and 4, no flow boundary was defined in the eastern boundary of the model domain because the mudstone of the Early Tertiary Yi’an group (E2+3y) outcrops along the eastern part of the study area. Given hydraulic head boundaries were defined in the northern and southern parts of the model area. Hydraulic head is considered constant at these boundaries because flow comes from these sides and the influence of well pumpage is marginal. The variable head boundary was defined in the western boundary of the model domain. The head values at these variable boundary nodes determined the head values of the observation wells and the Kriging estimation. The internal nodes were considered variable head nodes. The second layer was defined as the semi-pervious Q2 formation as shown in Fig. 2. Groundwater flow moves vertically with lower permeability and connects hydraulically between the upper aquifer and the deep aquifer in this layer. The third layer, representing the upper aquifer, has constant head as shown in Fig. 2, Q3. According to the groundwater level measurements from observation wells in January 1986, the initial hydraulic heads were determined by using Kriging interpolation. The groundwater flow model is calibrated by using an optimal estimate algorithm, 2D-KALFEFLOW, 2-D groundwater flow modeling of coupled finite-element and Kalman filter (Wu and Bian 2003).
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Fig. 4 Deterministic parameter subareas of the groundwater flow in the deep aquifer. Dots indicate observation wells; solid line, zero flux boundary; broken line, given hydraulic head boundary
Table 1 Deterministic parameters of the groundwater flow in the deep aquifer Subarea 1 2 3 4 5 6
K (m/d) 35 78 53 61 115 93
c (d)
S
200 185 150 160 100 120
Table 2 Stochastic parameters of the groundwater flow in the deep aquifer
0.01 0.015 0.001 0.002 0.015 0.013
Subarea
1 2 3 4
Subarea 7 8 9 10 11 12
K (m/d) 70 65 82 103 100 18
Standard deviation of system noise (m) 0.13 0.18 0.65 0.87
Subarea
5 6 7 8
Through the calibration of the groundwater flow model, aquifer parameters were obtained from an optimal estimate algorithm of the coupled finite element method and Kalman filtering and is shown in Table 1 and Table 2. It notes that K is the hydraulic conductivity of the deep confined aquifer, c is the hydraulic resistance of the semipervious layer, and S is the storage coefficient of the deep confined aquifer. The design of a groundwater monitoring network After the model was calibrated, the monitoring network density was analyzed by simulating the standard deviation surface (SDS) for several network configurations. The results of four simulations are given below. The locations of the observation wells from all simulations are shown in Figs. 5, 6, 7, and 8. Simulation A is the analysis of the existing monitoring network with 38 observation wells with the measurement frequency of 12 times per year. Figure 5 shows the spatial distribution of SDS of the existing monitoring network, which is used as a reference for the other simulations.
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c (d)
S
160 140 120 86 100 300
Subarea
0.004 0.001 0.065 0.075 0.075 0.05
Standard deviation of system noise (m) 0.27 0.49 0.54 0.14
K (m/d)
13 14 15 16 17 18
25 8.0 109 115 77 115
Subarea
Standard deviation of system noise (m)
9 10 11 12
0.20 0.32 0.09 0.12
c (d) 260 350 150 100 130 100
Subarea
13 14
S 0.04 0.05 0.09 0.09 0.04 0.09
Standard deviation (m) 0.51 0.72
From Fig. 5, it can be seen that all standard deviations in the northern part of the Daqing area are less than 0.5 m. This is due to the influence of low standard deviations of the system noise (0.13 to 0.17 m). The standard deviations in the southern part of the Daqing area are approximately equal to 0.5 m. The standard deviations in the western part of the Daqing area are more than 0.5 m, which is partly due to the influence of the boundaries. The standard deviations in the center and eastern parts of the Daqing area are more than 0.5 m, which is most likely due to the groundwater withdrawn from the wells. The average standard deviation in the whole area is 0.65 m, in which the high standard deviation is due to high stochastic parameters ranging from 0.09 to 0.87 m, an average of 0.32 m, as shown in Table 2. To understand the change process of the groundwater level under larger exploitation and abstraction, it is necessary to increase observation wells in the cone area of depression of groundwater level. The criterion based on the threshold value of SDS 0.5 m is applied to designing a monitoring network for the Daqing area. The area with SDS being greater than 0.5 m suggests
Original article
Fig. 5 Contour map of the SDS of the existing monitoring network of simulation A in meters. Dots represent observation wells (38 wells)
Fig. 6 Contour map of the SDS of the regular monitoring network of simulation B in meters. Dots represent observation wells (66 wells)
Fig. 7 Contour map of the SDS of the optimized monitoring network of simulation C in meters. Dots represent observation wells (88 wells)
Fig. 8 Contour map of the SDS of the alternative monitoring network of simulation D in meters. Dots represent observation wells (93 wells)
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Fig. 9 The relationship between the maximum information and the minimum cost
that the number of observation wells be increased and the area with SDS being less than 0.5 m suggests that the number of observation wells be decreased. Based on the analysis of the standard deviations for the existing monitoring network, multiple alternative plans was applied to selecting an optimal monitoring network for groundwater. Simulation B is a plan of the regular monitoring network with 66 observation wells with the measurement frequency of 12 times per year without the consideration of hydrogeologic conditions, in which observation wells were placed at regular distances of one well per 100 km2. Figure 6 shows the spatial distribution of SDS of the regular monitoring network with 66 observation wells with the measurement frequency of 12 times per year. From Fig. 6, it can be seen that the standard deviations in the northern part of the Daqing area are less than a given threshold value (0.50 m), and observation wells may be reduced. The standard deviations in the center and eastern parts of Daqing area, as the center of depression cone, are greater than a given threshold value (0.50 m), and observation wells may be increased. The standard deviations of the whole area range from 0.1 to 1.6 m and the average value is 0.59 m. Simulation C is an optimal monitoring network with 88 observation wells with the measurement frequency of 12 times per year. The number of observation wells in Simulation C was minimized for a given threshold value of the SDS (0.50 m). The resulting monitoring network consists of 88 observation wells with the measurement frequency of 12 times per year. From Fig. 7, it can be seen that the standard deviations of the whole area basically satisfy a given threshold value of SDS (0.50 m). The partly high standard deviations in the western, central and eastern parts are due to the influence of high system noise (0.54 to 0.87 m) and boundaries and cannot be decreased 534
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easily. The standard deviations of the whole area range from 0.1 to 1.0 m and the average value is 0. 50 m. To examine an optimized Simulation C, observation wells were increased to 93 in Simulation D. Figure 8 shows the spatial distribution of SDS of the alternative monitoring network with 93 observation wells with the measurement frequency of 12 times per year. From Fig. 8, it can be seen that in the comparison of Simulation C with Simulation D there is no significant improvement in standard deviations. The standard deviations of the whole area range from 0.1 to 1.0 m and the average value is 0.49 m. To effectively determine a threshold value of the SDS for the Daqing region of China, a method involving the rational trade-off between maximum-information and minimum cost was proposed. Maximum- information is equivalent to minimizing the error of prediction associated with the groundwater parameter estimates. For the minimum-cost network, the designer has an objective of minimizing the cost of collecting the data while attaining a specified level of regional accuracy. Minimum cost is equivalent to minimizing the number of observation wells. Through computing the standard deviations of estimation error for multiple alternative monitoring networks of groundwater, the relationship between the maximum information and the minimum cost is indicated in Fig. 9. From Fig. 9, the average standard deviations (0.59 m) in the regular monitoring network with 66 observation wells with the measurement frequency of 12 times per year are less than the those (0.58 m) in the alternative monitoring network with 59 observation wells with the measurement frequency of 12 times per year. The reason is that the distribution of observation wells does not consider hydrogeological conditions in the regular network, but the alternative network takes into account hydrogeological and pumpage conditions. As the number of observation wells in the alternative monitoring network increases from
Original article
Lecture Notes in Computer Science, Springer, Berlin Heidelberg 93 to 115 wells, the average standard deviations do not decrease significantly. Therefore, the optimal locations and New York, pp 34–56 Hsu NS, Cheng KW (2000) Network optimization flow model for frequency of observation well were determined with a basin-scale water supply planning. J Water Resour Pl-ASCE threshold value of the SDS (0.5 m) and 88 wells. 128(2):102–112
Summary and conclusions For a threshold value of 0.5 m for the SDS, the optimal monitoring network can be increased to 88 observation wells (one well/80 km2 ) with the measurement frequency of 12 times per year. The final design of the monitoring network is also based on other considerations including the continuing of existing or disused observation wells and the accessibility of the observation wells. Kalman filtering can be calculated for any arbitrary combination of network density and measurement frequency. This study has only worked out optimum network density for the measurement frequency of 12 times per year because of management reasons. This is a key problem in the determination of a threshold value of SDS. Based on the analysis of the existing monitoring network, the system noise, measurement error and cost conditions should be considered. In this paper, a method of the rational trade-off between maximuminformation and minimum cost was adopted for selecting a threshold value of SDS. Based on a threshold value of SDS and a multi-alternative monitoring network of groundwater, the optimal locations and frequency of observation well were determined. Acknowledgements This work was supported by a grant from the National Natural Science Foundation of China (90102003), the Innovation Project of CAS (KZCX1–10–03, KZCX210021) and the Project of Education Department of China (00233). The authors wish to thank the anonymous reviewers for their reading of the manuscript, and for their suggestions and critical comments.
References Adamouski K, Hamory T (1983) A stochastic systems model of groundwater level fluctuations. J Hydrol 62(1/4):129–141 Bogardi I, Bardossy A, Duckstein L (1985) Multicriterion network design using geostatistics. Water Resour Res 21:199–208 Bras RL (1979) Sampling of interrelated random fields: the rainfall-runoff case. Water Resour Res 15(6):1767–1780 Carrera J, Szidarovzsky F (1985) Numerical comparison of network design algorithms for regionalized variables. Appl Math Comput 16:189–202 Carrera J, Usunoff E, Szidarovszky F (1984) A method for optimal observation network design for ground water management. J Hydrol 73:147–163 Crawford KC (1979) Considerations for the design of a hydrologic data network using multivariate sensors. Water Resour Res 15(6):1752–1762 de Marsily G (1986) Quantitative hydrogeology. Academic, San Diego Dorn JL, Ranjithan S (2003) Evolutionary multiobjective optimization in watershed water quality management. In: Fonseca and others (eds) Evolutionary multi-criteria optimization.
Journel A, Huijbregts C (1978) Mining geostatistics. Academic, San Diego Knopman DS, Voss CI (1989) Multiobjective sampling design for parameter estimation and model discrimination in groundwater solute transport. Water Resour Res 25(10):2245–2258 Loaiciga HA (1989) An optimization approach for groundwater quality monitoring network design. Water Resour Res 25(8):1771–1782 Loaiciga HA, Charbeneau RJ, Everett LG, Fogg GE, Hobbs BF, Rouhani S (1992) Review of ground-water quality monitoring network design. J Hydraul Eng-ASCE 118(1):11–37 Made JW van der (1986) Design aspects of the hydrological networks. CHO Proceedings and Information No 35:172, WMO, Delft Pinder GF, Dougherty DE, Greenwald RM (2002) Optimization and modeling for remediation and monitoring. In: Chien CC and others (eds) Environmental modeling and management: theory, practice, and future directions. Dupont workshop on modeling and management of emerging environmental Issues, Philadelphia, pp 111–185 Prakash MR, Singh VS (2000) Network design for groundwater monitoring – a case study. Environ Geol 39(6):628–632 Reed PM (2002) Striking the balance: long-term groundwater monitoring design for multiple conflicting objectives. PhD Thesis, University of Illinois Rouhani S (1985) Variance reduction analysis. Water Resour Res 21(6):837–846 Solomatine DP (1999) Random search methods in model calibration and pipe network design. In: Savic D, Walters G (eds) Water industry system: modeling and optimization applications. Research Studies Press, Baldock, UK, pp 317–332 Spruill TB, Candela L (1990) Two approaches to design of monitoring networks. Ground Water 28(3):430–442 Van Geer FC (1982) An equation based theoretical approach to network design for groundwater levels using Kalman filters. Int Assoc Hydrol Sci Publ 136:241–250 Wilson JL, Kitanidis PK, Dettinger H (1978) State and parameter estimation in groundwater models. Proceedings of the American Geophysical Union Chapman Conference on Applications of Kalman Filter to Hydrology, Hydraulics, and Water Resources, Pittsburgh, pp 657–679 Wood EF, McLaughlin DB (1984) Groundwater monitoring well redesign. Paper presented at the NWWA/API conference on petroleum hydrocarbons and organic chemicals in groundwater: prevention, detection, and restoration, Natl Water Well Assoc, Houston Wu Y (1992) Optimal design of groundwater level observation network. PhD Thesis, Xi an College of Geology, Xi an, China, pp 70–80 (in Chinese) Wu Y, Bian N (2003) Optimal analysis of groundwater monitoring network of a karst aquifer. Earth Science Frontiers, No 3, (In Press, In Chinese) Zhou Y, Te Stroot CBM, Van Geer FC (1991) Using Kalman filtering to improve and quantify the uncertainty of numerical groundwater simulations 2: Application to monitoring network design. Water Resour Res 27(8):1995–2006 Zhou Y, Van Geer FC (1992) KALMOD, a stochastic-deterministic model for simulating groundwater flow with Kalman filtering. J Sci Hydrologiques 37(4):375–389 Zidek JV, Sun WM, Le ND (2000) Designing and integrating composite network for monitoring multivariate Gaussian pollution fields. J Roy Stat Soc C-Applied Statistics 49:63–79
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